Question

what is the derivative of 2sinx and 2cos2x? i need to find the rules in finding derivative of such functions.

Answer 1

know chain rule ?

Answer 2

for 2sin x
its just 2 cos x because the constant '2' can be taken out of derivative.

Answer 3

product rule shows up somewhere. i know 2sinx = 2cosx and 2cos2x = -4sin2x

Answer 4

*** i mean chain...rule.

Answer 5

yes, to differentiate cos 2x ,you need chain rule, know what is it ?

Answer 6

i know what it is but i don't know how to apply it to cos2x. i can work it on something like f(x) = (3x+4)^5 but not cos2x

Answer 7

d/dx [cos 2x] = [-sin 2x] d/dx [2x]
there's an inner function, and there's an outer function.
d/dx composite = d/dx outer * d/dx inner
here, outer = cos , inner =2x

Answer 8

like in f(x) = (3x+4)^5
outer = x^5
inner = 3x+4

Answer 9

so, you multiply 5(3x+4)^4 by d/dx(3x+4), right ?
similarly,here you multiply by d/dx [2x]
making any sense ? :P

Answer 10

so i can say 2tan2x = 4sec^2x and tan2x = 2sec^2x? right?

Answer 11

yes! correct :)

Answer 12

thanks :)